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What is the derivative of # f(x) = (arctan (x/2)) + ((5x-1)/(2(x^2) + 4))#?

1 Answer

Jun 3, 2018

#f'(x)=2/(4+x^2)+(-10*x^2+4x+20)/(2*x^2+4)^2#

Explanation:

Note that
#(arctan(x))'=1/(1+x^2)#
so we get

#f'(x)=1/(1+x^2/4)*1/2+(5*(2x^2+4)-(5*x-1)*4x)/(2x^2+4)^2#

so we get

#f`(x)=2/(4+x^2)+(-10*x^2+4x+20)/(2*x^2+4)^2#

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